1. For the holiday weekend, a fireworks display is being set up to be launched off of a hill so they will be displayed over the lake. The path of the “Big Boom” firework is modeled by the quadratic relation, h = − 5t2 + 40t + 3 . The path of the “Sparkle Sensation” firework is modeled by the quadratic relation, h = − 4t2 + 24t +3. In both relations h represents the height of the firework above the water, in meters, after t seconds.
a. How high above water level is the hill where the “Big Boom” firework was launched.
b. The fireworks are designed to display at their maximum height. How high above the water is the “Big Boom” firework when it is displayed?
c. The “Sparkle Sensation” firework is designed to go off at a lower height than the “Big Boom” firework. What is the difference in the heights of the two fireworks?
d. The organizers would like both fireworks to go off at the same time. Which firework should be set off first? How long after the first one is launched, should the second one be launched?
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